Can you open a command prompt window? If so try starting a program from the command prompt. You can also try starting programs from the taskmanager. One of these tricks may get you around a hack of explorer. Another from explorer, a shift-Run As sometimes works to start a blocked exe

There is at least one trojan that adds a gazillion entries in a registry key that effectively blocks all exe programs.

If you haven't already seen it maybe this google search will be helpful.